Anomaly detection in random fields is an important problem in many applications including the detection of cancerous cells in medicine, obstacles in autonomous driving and cracks in the construction material of buildings. Such anomalies are often visible as areas with different expected values compared to the background noise. Scan statistics based on local means have the potential to detect such local anomalies by enhancing relevant features. We derive limit theorems for a general class of such statistics over M-dependent random fields of arbitrary but fixed dimension. By allowing for a variety of combinations and contrasts of sample means over differently-shaped local windows, this yields a flexible class of scan statistics that can be tailored to the particular application of interest. The latter is demonstrated for crack detection in 2D-images of different types of concrete. Together with a simulation study this indicates the potential of the proposed methodology for the detection of anomalies in a variety of situations.

翻译：随机场中的异常检测是许多应用领域中的重要问题，包括医学中癌细胞的检测、自动驾驶中的障碍物识别以及建筑材料裂缝的发现。此类异常通常表现为与背景噪声存在不同期望值的区域。基于局部均值的扫描统计量通过增强相关特征具有检测此类局部异常的潜力。我们推导了一类适用于任意固定维度M相依随机场的广义扫描统计量的极限定理。通过允许对不同形状局部窗口内的样本均值进行多种组合与对比，该方法构建了可针对特定应用场景灵活调整的扫描统计量族。该方法的实用性在两类混凝土二维图像的裂缝检测中得到了验证。结合模拟研究，这表明所提出的方法在多种场景的异常检测中具有应用潜力。